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Operations Management Inventory Management. The Functions of Inventory. To have a stock of goods that will provide a “selection” for customers To take advantage of quantity discounts To hedge against inflation and upward price changes. Disadvantages of Inventory. Higher costs
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The Functions of Inventory • To have a stock of goods that will provide a “selection” for customers • To take advantage of quantity discounts • To hedge against inflation and upward price changes
Disadvantages of Inventory • Higher costs • Item cost (if purchased) • Ordering (or setup) cost • Costs of forms, clerks’ wages etc. • Holding (or carrying) cost • Building lease, insurance, taxes etc. • Difficult to control • Hides production problems
Types of Inventory • Raw material • Work-in-process (WIP) • Maintenance/repair/operating supplies (MRO) • Finished goods
Inventory Management Two ingredients of inventory mgmt systems • Classification of inventory items • Basis for establishing inventory policies • Maintenance of accurate inventory records
ABC Analysis • Divides on-hand inventory into 3 classes • A class, B class, C class • Basis is usually annual $ volume • $ volume = Annual demand x Unit cost • A (70%-80% of total annual $ volume); B (15-25%), C (5%) • Other criteria could include • Delivery problems • Quality problems • High unit cost
% Annual $ Usage Class % $ Vol % Items A 80 15 100 B 15 30 80 C 5 55 60 A 40 B C 20 0 0 50 100 % of Inventory Items Classifying Items as ABC
ABC Analysis • Policies then established for each class after analysis • Policies based on ABC analysis could include • Focus more on development of class A suppliers • Have tighter physical control of A items • Forecast A items more carefully
Independent versus Dependent Demand • Independent demand - demand for item is independent of demand for any other item • Demand for cars is independent of demand for TV’s • Dependent demand - demand for item is dependent upon the demand for some other item • Demand for car tires is dependent on demand for cars
Inventory Costs • Holding costs - associated with holding or “carrying” inventory over time • Ordering costs - associated with costs of placing order and receiving goods • Setup costs - cost to prepare a machine or process for manufacturing an order
Inventory Models • When to order and how much to order • Fixed order-quantity models • Economic order quantity • Production order quantity • Quantity discount • Probabilistic models
EOQ Assumptions • Known, constant and independent demand • Known and constant lead time • Instantaneous and complete receipt of material • No quantity discounts • Only order (setup) cost and holding cost considered
Order quantity = Q (maximum inventory level) Usage Rate AverageInventory (Q*/2) Inventory Level Minimum inventory 0 Time Inventory Usage Over Time
Annual Cost Total Cost Curve Holding Cost Curve Minimum total cost Order (Setup) Cost Curve Order quantity Optimal Order Quantity (Q*) EOQ ModelHow Much to Order?
Deriving an EOQ • Develop an expression for setup or ordering costs • Develop an expression for holding cost • Set setup cost equal to holding cost • Solve the resulting equation for the best order quantity
Inventory Level AverageInventory (Q*/2) Optimal Order Quantity(Q*) Reorder Point (ROP) Time Lead Time EOQ Model When To Order
Q* Slope = units/day = d Inventory level (units) ROP (Units) Time (days) Lead time = L The Reorder Point (ROP) Curve
Production Order Quantity Model • Answers how much to order and when to order • Allows partial receipt of material – no instantaneous receipt of materials • Other EOQ assumptions apply • Suited for production environment • Material produced, used immediately • Provides production lot size • Lower holding cost than EOQ model
Production Order Quantity Model Answers how much to order and when to order Allows partial receipt of material – no instantaneous receipt of materials Other EOQ assumptions apply Suited for production environment Material produced, used immediately Provides production lot size Lower holding cost than EOQ model
Quantity Discount Model Answers how much to order & when to order Allows quantity discounts Reduced price when item is purchased in larger quantities Other EOQ assumptions apply Trade-off is between lower price & increased holding cost
Quantity Discount Model Compute the common EOQ and identify the feasible range. If the feasible EOQ is on the lowest price range, that is the optimal order quantity. If the EOQ isbelow the allowable range, adjust the EOQ to the lowest price break qty of that range If the EOQ is above the allowable range, discard that EOQ Compare the total costs (including total cost of product) for the feasible EOQ and price break quantity. Select the quantity that yields the lowest total costs.
Probabilistic models When demand is not known, but can be expressed as a probabilistic distribution Uncertain demand raises possibility of stock out Service level – complement of probability of stock out